Well all this is true %100 of the time:
> If you check he will bet all hands in his distribution.
> If you bet the flop, he will call with all hands in his distribution.
> If you check raise the flop he will call the check raise with all hands.
...then there's no point in continuing unless we can make him fold on the turn. If he's going to continue with his hand regardless what we do, then there's no point putting in our money when we're behind every hand in his distribution.
We should be check-folding. If
we can consider the turn aswell (as a possibility for a second bullet) then maybe a check-raise might be best followed by a big bet on the turn to possibly make him fold, but I don't like making this play unless he's going to respect it with KK-TT hands and possibly AQ.